16.7 ROOT LOCUS ANALYSIS

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It is possible to have systems that are unstable. For example, think of a washing machine that vibrates so much that it `walks' across a floor. Or many high speed aircraft that fail due to resonant vibrations.

To analyze these problems Root-Locus Plots can be used.

The first step in creating a root-locus plot is to break the equation into roots and poles.

The next step in creating a root locus plot is to calculate values for the roots, based on varying system parameters.

These values can then be plotted to give the root locus plot (used for design).

The use of the root locus plots is to estimate the system performance. For example the system with two roots above will give the following root locus plots, and the corresponding real time responses.

Note that the last two cases are unstable, and that they have roots in the right hand side of the complex plane